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Quantum Storage of Photonic Entanglement in a Crystal
Christoph Clausen, Imam Usmani, Felix Bussieres, Nicolas Sangouard, Mikael Afzelius, Hugues de Riedmatten, Nicolas Gisin
TL;DR
The paper addresses whether photonic entanglement can be transferred to a material quantum memory, an important capability for quantum communication technologies. It stores one photon of an entangled pair in a crystal using an atomic frequency comb and verifies the transferred entanglement through a CHSH violation of S = 2.64 ± 0.23.
Problem
The work investigates entanglement between a telecommunication-wavelength photon and a collective atomic excitation stored in a crystal for quantum communication applications.
Method
An atomic frequency comb in a neodymium-doped Y2SiO5 crystal stores one photon from an entangled pair and re-emits it after a predetermined time while the telecom photon travels through a fiber link for analysis.
Results
S = 2.64 ± 0.23, a direct violation of the CHSH inequality showing nonlocal quantum correlations between the telecom photon and a collective atomic excitation.
Takeaways & Limitations
The demonstrated light–matter entanglement supports efforts toward solid-state quantum communication technologies and efficient quantum repeaters for long-distance networks.
Takeaways & Limitations
The hybrid-qubit CHSH analysis uses a fair sampling assumption, discarding inconclusive results.
Abstract
from arXiv · showhide
Entanglement is the fundamental characteristic of quantum physics. Large experimental efforts are devoted to harness entanglement between various physical systems. In particular, entanglement between light and material systems is interesting due to their prospective roles as "flying" and stationary qubits in future quantum information technologies, such as quantum repeaters and quantum networks. Here we report the first demonstration of entanglement between a photon at telecommunication wavelength and a single collective atomic excitation stored in a crystal. One photon from an energy-time entangled pair is mapped onto a crystal and then released into a well-defined spatial mode after a predetermined storage time. The other photon is at telecommunication wavelength and is sent directly through a 50 m fiber link to an analyzer. Successful transfer of entanglement to the crystal and back is proven by a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by almost three standard deviations (S=2.64+/-0.23). These results represent an important step towards quantum communication technologies based on solid-state devices. In particular, our resources pave the way for building efficient multiplexed quantum repeaters for long-distance quantum networks.
EXPERIMENT
The experiment combines a rare-earth-crystal AFC memory with an energy-time-entangled photon source, using filtered 883 nm signal photons for storage and 1338 nm idler photons for direct analysis.
- EXPERIMENT: The setup integrates a crystal quantum memory, AFC-preparation lasers, and a spectrally filtered entangled-photon source.The system alternates 15 ms of AFC preparation with 15 ms of photon-storage measurement.
- EXPERIMENT: Energy-time-entangled photons are generated by continuous-wave 532 nm-pumped SPDC, with signal and idler wavelengths of 883 nm and 1338 nm.Both photons initially have approximately 1.5 THz bandwidth, far exceeding the memory bandwidth and requiring strong filtering.
- EXPERIMENT: The AFC memory uses a neodymium-doped Y2SiO5 crystal to absorb and collectively re-emit photons into a defined spatial mode after a predetermined delay.The comb is prepared by optical pumping, and the re-emission time is set by the comb period.
- EXPERIMENT: The AFC interface supports storage of true single photons generated at random times because it can coherently store multiple temporal modes.Applying it to SPDC photons requires elaborate filtering, frequency stabilization, and increased storage efficiency.
Non-classical correlations
The study tests whether photon correlations survive storage and retrieval in the crystal. Cross-correlations remain nonclassical through 200 ns, while storage efficiency decreases with longer delays.
- Non-classical correlations: Cross-correlations remain well above the classical regime for storage times up to 200 ns.Longer storage makes optimal comb preparation more difficult because of material limitations, reducing efficiency and cross-correlation.
- Non-classical correlations: g(2)si provides a criterion for non-classicality based on intensity correlations between the signal and idler modes.The relevant coincidence and single-detection probabilities are estimated inside and outside the coincidence peak.
- Non-classical correlations: The experiment measures cross-correlation versus pump power and storage time, comparing AFC preparation with a 120 MHz transmission window without AFC.Low pump powers are limited by detector dark counts, while high powers suffer from multiple-pair contributions.
- Non-classical correlations: g(2)si ≃30 after 25 ns of storage proves that the storage process preserves quantum correlations.The reduction is attributed to limited 21% efficiency, which increases accidental coincidences from dark counts and multiple-pair emissions.
Entanglement
A Franson-type interference experiment shows that energy-time entanglement survives storage of the signal photon in the crystal. The retrieved state retains sufficient fidelity for a direct CHSH-inequality violation.
- Franson interference: A Franson-type setup tests energy-time entanglement using a fiber interferometer for the idler and partial memory read-outs for the signal.The signal read-outs correspond to short and long storage times separated by τ = 25 ns.
- Franson interference: τ = 25 ns separates three coincidence-histogram peaks corresponding to short-short, short-long or long-short, and long-long path combinations.Interference appears in the central peak as the signal and idler relative phases vary.
- Entanglement preservation: V = 84 ± 4% and 78 ± 4% are the measured interference visibilities, corresponding to mean two-qubit fidelity F = 86 ± 2%.The visibility measurements use a source pump power of 5 mW.
- Entanglement preservation: F ≥ 0.5 under the Peres criterion establishes that the two photons remain entangled after quantum storage.The entangled partner of the telecom photon is a collective atomic excitation inside the memory while the signal photon is stored.
- Bell test: S = 2.64 ± 0.23 directly violates the CHSH inequality, demonstrating nonlocal quantum correlations between the telecom photon and the collective atomic excitation.The result establishes entanglement independently of the experimental details.
Bell test involving hybrid qubit
A second Bell test treats one transmitted and one retrieved temporal mode as a hybrid qubit. The measured violation demonstrates preservation of the initial entanglement through the storage process.
- Hybrid-qubit construction: A single read-out combined with the transmitted part of the photon forms temporal modes for a hybrid-qubit CHSH analyzer.The imbalance between storage efficiency and transmission probability supplies the analyzer in bases lying in the xz-plane of the Bloch sphere.
- Bell test: S = 2.62 ± 0.15 violates the CHSH inequality by more than 4 standard deviations.This measurement uses the single-read-out and transmitted temporal modes rather than two partial read-outs.
- Interpretation: The violation witnesses preservation of the initial entanglement at every step before detection.The resulting state is entangled between a telecom-wavelength qubit and a photon-crystal hybrid qubit.
- Relevance: The photon-crystal hybrid qubit is identified as a key ingredient of an efficient quantum repeater based on atomic ensembles and linear optics.
OUTLOOK
The experiment demonstrates that commercial rare-earth-doped crystals can store entangled photons, supporting solid-state quantum-repeater development. Longer storage, on-demand read-out, and higher efficiency remain major challenges.
- OUTLOOK: Entanglement between a photon and a collective atomic excitation delocalized over a 1 cm crystal is demonstrated.
- OUTLOOK: Commercial crystals can serve as quantum memories for entangled photons, an enabling step toward solid-state quantum repeaters.
- Challenges: Longer storage times, on-demand read-out, and higher efficiency are identified as the next major challenges.
- Possible improvements: Longer crystals or optical cavities are proposed to increase effective interaction length and address efficiency limitations linked to optical depth.
- Related work: Saglamyurek et al. independently demonstrated storage and retrieval of an entangled photon using a thulium-doped lithium niobate waveguide.
Atomic Frequency Comb
The atomic frequency comb memory reshapes a crystal’s absorption spectrum into periodic peaks that absorb and collectively rephase photons for predetermined re-emission. Square-shaped comb peaks improve efficiency, while longer storage is limited by material coherence.
- AFC principle: An AFC shapes the crystal absorption profile into a comb-like structure using optical pumping, exploiting high atomic density despite inhomogeneous broadening.
- AFC principle: A photon is absorbed into a collective atomic excitation delocalized over the ensemble and later re-emitted in a well-defined spatial mode.
- AFC timing: ts = 1/∆ determines the re-emission time because periodic atomic detunings rephase after one comb period.
- Performance: 21% efficiency at ts = 25 ns and 12% at ts = 100 ns are achieved using approximately square comb peaks prepared by incoherent optical pumping.
- Spectrum: The AFC spans a 120 MHz bandwidth, with peak widths larger than the effective material linewidth to use the available optical depth.
- Limitations: Longer storage reduces efficiency because material coherence limitations deteriorate the comb shape for closely spaced peaks.
Spectral filtering of photon pairs
The setup uses sequential spectral filtering to narrow photon bandwidths and suppress spurious modes and accidental coincidences. Detection efficiencies are low, especially at the telecom wavelength.
- At 1338 nm, a Fabry–Perot cavity and Fiber Bragg grating narrow the photons to a final linewidth of 45 MHz and remove additional cavity modes.The cavity has a 23.9 GHz free spectral range, while the grating has a 16 GHz spacing.
- At 883 nm, two etalons with approximately 600 MHz bandwidths and different free spectral ranges suppress spurious longitudinal modes.The etalons have free spectral ranges of 42 and 50 GHz.
- The crystal provides additional filtering outside the AFC’s 120 MHz bandwidth, reducing contributions from its 6 GHz inhomogeneous absorption profile.
- Detection efficiencies are approximately 0.15% at 1338 nm and 0.5% at 883 nm, including switch and optical-element losses.Detector efficiencies are 8% and 10% at 1338 nm, and 30% at 883 nm; dark counts are 10 Hz and 100 Hz, respectively.
Measurements and frequency stabilization
Measurements alternate AFC preparation with photon-storage measurements, while coincidence acquisition requires long-term frequency and phase stabilization. The setup reduces long-term AFC–photon frequency deviations to about 1 MHz.
- Each experimental cycle uses 15 ms for AFC preparation and frequency stabilization, followed by 15 ms of photon-storage measurement.A fiber-optic switch alternates between preparation and measurement, while optical shutters protect the detector from preparation light.
- Coincidence statistics measure the time between telecom-photon detection and detection of its 883 nm partner, with typical rates of a few coincidences per minute.Accumulation times reached several hours, requiring stable lasers and filtering elements.
- The telecom interferometer phase was stabilized with highly coherent difference-frequency-generation light.
CHSH inequality with partial read-outs
The partial-readout Bell test analyzes energy-time entanglement using two temporal modes and interferometric measurements. Appropriate signal and idler bases produce a CHSH violation after memory storage and retrieval.
- Energy-time entanglement is treated as two temporal modes, early and late, separated by a delay τ exceeding the individual-mode coherence time.
- A fiber interferometer analyzes the idler, while partial read-outs of the quantum memory implement the signal interferometer.
- The CHSH test uses signal bases X1 and X2 and idler bases Y1 and Y2, with 90° separation between X1 and X2 and 45° rotations for the idler bases.All four bases lie on the Bloch-sphere equator because the short- and long-path detection probabilities are equal.
- Four measurements per correlator were required because each side had only one detector, yielding 16 measurements for the Bell test.
- S = 2.64 ± 0.23, demonstrating a CHSH violation and entanglement between the telecom photon and a collective atomic excitation in the crystal.The uncertainty is a standard deviation associated with Poissonian coincidence statistics.
CHSH inequality with a hybrid qubit
The hybrid-qubit test combines a telecommunication-wavelength time-bin qubit with a photon–crystal hybrid qubit formed by storage and transmission. By adjusting the AFC and analyzing in suitable bases, the experiment observes a strong CHSH violation.
- The hybrid qubit is a superposition of a single collective atomic excitation in the crystal and a photonic signal state, paired with a telecom time-bin qubit.
- The early signal mode is stored and released after exactly τ, making its echo indistinguishable from the directly transmitted late mode.
- The AFC controls the signal phase, using φs,1 = 0° and φs,2 = 180° for the two signal measurements.
- The telecom photon is measured in the z direction by arrival time or in the x direction with a Michelson interferometer.
- S = 2.62 ± 0.15, violating the CHSH inequality by more than 4 standard deviations and showing entanglement of the hybrid and telecom qubits.The analysis uses a generalized measurement and discards inconclusive results under the fair-sampling assumption.